1.Cf. Oldenburg's remark on behalf of others in Ep74, “If
this [necessitarianism] is conceded and affirmed, they say, the sinews
of all law, all virtue and religion are severed,” and Jonathan
Bennett's remark: “This implies that every particular proposition
is itself necessary, that being the dangerously false thesis towards
which his explanatory rationalism is pushing him” (Bennett
(1984), 121, emphasis mine).

2.
For the most part, I will ignore the thorny issue of how to fit the
attributes into Spinoza's ontology. Spinoza claims that attributes
somehow constitute the essence of substance (Id4), and in Ip4d he even
suggests that the attributes are identical to substance itself, though
it is far from obvious how to understand this one-to-many identity
claim.

3.
See also Iax4, Iax5, and Ip3d. The pesky PSR question of what is it in
virtue of which these conceptual relations obtain is a
difficult one. Leibniz was inclined towards an answer in terms of
asymmetrical containment: y conceptually depends on x
in virtue of the containment of the concept of y in the
concept of x. Spinoza once glosses conceptual relations in
terms of containment in passing (C 245), but he fails to develop this
idea further, and instead he usually relies on the more ambiguous
description of conceptual “involvement.”

4.
Spinoza's argument for (12) invokes an a posteriori claim that
something or other exists (he uses “we exist” in Ip11d, but
any existing thing will work). His argument is that (a) something
exists; (b) everything that exists exists either in itself (substances)
or in another (modes) (Iax1); (c) it is impossible for something that
is in another to exist unless that in which it inheres also exists (Ip1
and Ip11d). Spinoza then runs a simple argument by cases: (d′) If
a substance is among the things existing in (a), then a substance
exists. (d″) If a mode is among the things existing in (a), then
a substance exists. Conclusion: since, by (b) only substances and modes
exist, it follows from (a)-(d) that at least one substance exists. (The
basis for (d′) is obvious. The basis for (d″) is the fact
that modes inhere in substances and (c).)

6.
This version is taken from Leibniz's early Confessiophilosophi (Leibniz 2005, 29), but there are many variations
of it across Leibniz's corpus. For a recent discussion of Leibniz's
views on perfection and harmony, see Strickland (2006).

7.
For the most well known version of the “category mistake”
objection (as well a discussion of other problems with the
property/mode reading), see Curley (1969). For a recent defense, see
Melamed (2009).

8.
For a recent attempt to connect Spinoza's infinite modes with
other pieces of his ontology (notably formal essences), see
Garrett 2009.

9. Although the terminology
can be misleading, these are not two distinct species or kinds of
necessity, whatever that may mean. The same distinction can be made
using only the contemporary “□” to stand for the
single kind of necessity. The important point is that y
necessarily following from something else does not by itself
make y's existence necessary. In propositional terms,
the hypothetical/absolute distinction is sometimes expressed as the
necessity of the
consequence vs. the necessity of the consequent.

10.
Spinoza will also need to rule out AP3, the possibility that
infinite modes could not have had different characteristics than they
in fact have. But Spinoza seems to think that effects are wholly
determined by their causes in the sense that both their
existence and their characteristics necessarily follow from their
causes. There are no fully self-determining features of modes;
everything about a mode is at least partly determined by its causes. In
the case of infinite modes, since those causes are themselves
absolutely necessary, this means that both the existence and
characteristics of infinite modes are absolutely necessary. Hence AP3
will not be a genuine alternative possibility for infinite modes. If
Curley is correct that the infinite modes are ontological expressions
of the laws of nature (at different levels of generalization), denying
AP3 would amount to denying that the laws of nature could have been
different than they in fact are.

11.
Leibniz appears to have read Spinoza's Ip28 in this way (Leibniz 1969,
203). For further discussion of Leibniz's reading of Spinoza, see
Laerke 2008.

12.
Curley develops his rejection of necessitarianism further in Curley and
Walski, 1999. For an alternative defense of the non-necessitarian
interpretation of Spinoza, see Martin 2010. Martin tries to restrict
the scope of Ip16 to infinite modes and also defends what I called the
“cursory reading” of Ip28.

13.
Leibniz develops this PSR point nicely (Leibniz 1969, 486), though the
conclusions he reaches from it are very different from Spinoza's.

14.
Notice that, if the entire collection of finite modes is itself an
infinite mode, a suggestion Garrett makes, the distinction between [ii]
and [iii] would collapse.

15.
This sentiment
is nicely expressed by one J. Jackson in 1734: “When it appears
that an absolute necessity in the nature of things themselves is the
reason and ground of their being what they are, we must necessarily
stop at this ground and reason; and to ask what is the reason of this
reason which is in the nature of things the last of all reasons, is
absurd” (quoted in Lovejoy 1936, 148).

16.
Incidentally,
this provides Spinoza a basis from which to criticize some forms of
contemporary anti-essentialism, according to which cheaply made
conceptual (or, more likely, analytical) connections between objects
and properties are sufficient and jointly necessary for metaphysically
determining modal facts (Newlands forthcoming).

17.
Although it is a minority
opinion today, interpreting Spinoza as denying the existence of finite
things has a rich pedigree. For recent discussions of this charge of
“acosmism,” see Melamed 2010 and Newlands 2011.

18.
It also allows us to answer Bennett's similar questions (Bennett 1984, 123).